In an ideal optical system as described theoretically by paraxial optics, all light rays emitted by a point source converge to a single point in the focal plane, forming a clear and sharp image. Departures of an optical system from this behavior are called aberrations, causing unwanted blurring of the image.
Manufacturers of photographic lenses attempt to minimize optical aberrations by combining several lenses. The design and complexity of a compound lens depends on various factors, e.g., aperture size, focal length, and constraints on distortions. Optical aberrations are inevitable and the design of a lens is always a trade-off between various parameters, including cost.
Similarly, when an astronomical object is observed from the surface of the earth, its emitted or reflected light has to pass through the atmosphere, which yields a blurry observed image. Deblurring images of an observed celestial body is therefore a fundamental problem in Astronomy. This problem is compounded by the fact that the blur is not only unknown, but is also continually changing in time as well as spatially due to refraction-index fluctuations caused by atmospheric turbulence. It is well known, that exposure times on a time scale where the turbulences are stationary (i.e. shorter than a tenth of a second) yield images that contain high-frequency information of the celestial object under investigation. This fact is exploited in Speckle Imaging, which is a collection of various techniques and algorithms for recovering high frequency information encapsulated in short-time exposure images. Due to the stochastic nature of atmospheric turbulence, Speckle Imaging techniques have to take a large number of images into account to actually regain diffraction-limited information.
In Speckle Interferometric Imaging short-exposure pictures are processed in Fourier domain. Through new developments in CCD technology which provide superior signal-to-noise ratio (Electron Multiplying CCD cameras), in recent years so-called Lucky Imaging methods have become popular. Usually a large number of images
(>10000) is collected, of which only a very small percentage is utilized to yield one high quality image. Different registration and super-resolution methods have been proposed for combination of the selected images.
Camera shake, on the other hand, is a common problem of handheld, longer exposed photographs occurring especially in low light situations, e.g., inside buildings. With a few exceptions such as panning photography, camera shake is unwanted, since it often destroys details and blurs the image.
The effects of optical aberrations on a lens, of atmospheric blur or camera shake, and many others, can be expressed (or sometimes at least approximated) as linear transformations of true sharp of time image that may be written as a matrix vector-multiplication (MVM)y=Ax  (1)where x is a vector representing the sharp or true image, y is an observed image, and A is the matrix expressing the linear image transformation.
However, estimating A given both x and y is computationally prohibitive in the general case. It is therefore desirable to restrict the solution space adequately, i.e. without overly sacrificing expressiveness, in order to efficiently perform MVMs, because these are the essential operations for blind deconvolution algorithms.
It is therefore an object of the invention to provide methods for handling the effects of optical aberrations, camera shake or atmospheric blur that can be implemented efficiently and possibly executed online.